Pertanyaan

Jika f ( x ) = 3 ( x 2 + 4 x + 6 ) 4 dan ∫ ( x + 2 ) ( x 2 + 4 x + 6 ) 3 dx = k ⋅ f ( x ) + c dengan k 1 = n ! untuk n bilangan asli, n=...

Jika $f (x) = 3 (x^{2} + 4 x + 6)^{4}$ dan $\int (x + 2) (x^{2} + 4 x + 6)^{3} dx = k \cdot f (x) + c$ dengan $\frac{1}{k} = n!$ untuk n bilangan asli, n=...

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Jawaban terverifikasi

Pembahasan

$straight f open parentheses straight x close parentheses equals 3 open parentheses straight x squared plus 4 straight x plus 6 close parentheses to the power of 4 straight f apostrophe open parentheses straight x close parentheses equals 24 open parentheses straight x plus 2 close parentheses open parentheses straight x squared plus 4 straight x plus 6 close parentheses cubed integral open parentheses straight x plus 2 close parentheses open parentheses straight x squared plus 4 straight x plus 6 close parentheses cubed dx equals integral fraction numerator straight f apostrophe open parentheses straight x close parentheses over denominator 24 end fraction dx equals fraction numerator straight f open parentheses straight x close parentheses over denominator 24 end fraction plus straight c 1 over straight k equals 24 equals 4 factorial straight n equals 4$